// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_BASIC_PRECONDITIONERS_H
#define EIGEN_BASIC_PRECONDITIONERS_H

namespace Eigen {

/** \ingroup IterativeLinearSolvers_Module
  * \brief A preconditioner based on the digonal entries
  *
  * This class allows to approximately solve for A.x = b problems assuming A is a diagonal matrix.
  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
    \code
    A.diagonal().asDiagonal() . x = b
    \endcode
  *
  * \tparam _Scalar the type of the scalar.
  *
  * \implsparsesolverconcept
  *
  * This preconditioner is suitable for both selfadjoint and general problems.
  * The diagonal entries are pre-inverted and stored into a dense vector.
  *
  * \note A variant that has yet to be implemented would attempt to preserve the norm of each column.
  *
  * \sa class LeastSquareDiagonalPreconditioner, class ConjugateGradient
  */
template <typename _Scalar> class DiagonalPreconditioner
{
    typedef _Scalar Scalar;
    typedef Matrix<Scalar, Dynamic, 1> Vector;

public:
    typedef typename Vector::StorageIndex StorageIndex;
    enum
    {
        ColsAtCompileTime = Dynamic,
        MaxColsAtCompileTime = Dynamic
    };

    DiagonalPreconditioner() : m_isInitialized(false) {}

    template <typename MatType> explicit DiagonalPreconditioner(const MatType& mat) : m_invdiag(mat.cols()) { compute(mat); }

    EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_invdiag.size(); }
    EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_invdiag.size(); }

    template <typename MatType> DiagonalPreconditioner& analyzePattern(const MatType&) { return *this; }

    template <typename MatType> DiagonalPreconditioner& factorize(const MatType& mat)
    {
        m_invdiag.resize(mat.cols());
        for (int j = 0; j < mat.outerSize(); ++j)
        {
            typename MatType::InnerIterator it(mat, j);
            while (it && it.index() != j) ++it;
            if (it && it.index() == j && it.value() != Scalar(0))
                m_invdiag(j) = Scalar(1) / it.value();
            else
                m_invdiag(j) = Scalar(1);
        }
        m_isInitialized = true;
        return *this;
    }

    template <typename MatType> DiagonalPreconditioner& compute(const MatType& mat) { return factorize(mat); }

    /** \internal */
    template <typename Rhs, typename Dest> void _solve_impl(const Rhs& b, Dest& x) const { x = m_invdiag.array() * b.array(); }

    template <typename Rhs> inline const Solve<DiagonalPreconditioner, Rhs> solve(const MatrixBase<Rhs>& b) const
    {
        eigen_assert(m_isInitialized && "DiagonalPreconditioner is not initialized.");
        eigen_assert(m_invdiag.size() == b.rows() && "DiagonalPreconditioner::solve(): invalid number of rows of the right hand side matrix b");
        return Solve<DiagonalPreconditioner, Rhs>(*this, b.derived());
    }

    ComputationInfo info() { return Success; }

protected:
    Vector m_invdiag;
    bool m_isInitialized;
};

/** \ingroup IterativeLinearSolvers_Module
  * \brief Jacobi preconditioner for LeastSquaresConjugateGradient
  *
  * This class allows to approximately solve for A' A x  = A' b problems assuming A' A is a diagonal matrix.
  * In other words, this preconditioner neglects all off diagonal entries and, in Eigen's language, solves for:
    \code
    (A.adjoint() * A).diagonal().asDiagonal() * x = b
    \endcode
  *
  * \tparam _Scalar the type of the scalar.
  *
  * \implsparsesolverconcept
  *
  * The diagonal entries are pre-inverted and stored into a dense vector.
  *
  * \sa class LeastSquaresConjugateGradient, class DiagonalPreconditioner
  */
template <typename _Scalar> class LeastSquareDiagonalPreconditioner : public DiagonalPreconditioner<_Scalar>
{
    typedef _Scalar Scalar;
    typedef typename NumTraits<Scalar>::Real RealScalar;
    typedef DiagonalPreconditioner<_Scalar> Base;
    using Base::m_invdiag;

public:
    LeastSquareDiagonalPreconditioner() : Base() {}

    template <typename MatType> explicit LeastSquareDiagonalPreconditioner(const MatType& mat) : Base() { compute(mat); }

    template <typename MatType> LeastSquareDiagonalPreconditioner& analyzePattern(const MatType&) { return *this; }

    template <typename MatType> LeastSquareDiagonalPreconditioner& factorize(const MatType& mat)
    {
        // Compute the inverse squared-norm of each column of mat
        m_invdiag.resize(mat.cols());
        if (MatType::IsRowMajor)
        {
            m_invdiag.setZero();
            for (Index j = 0; j < mat.outerSize(); ++j)
            {
                for (typename MatType::InnerIterator it(mat, j); it; ++it) m_invdiag(it.index()) += numext::abs2(it.value());
            }
            for (Index j = 0; j < mat.cols(); ++j)
                if (numext::real(m_invdiag(j)) > RealScalar(0))
                    m_invdiag(j) = RealScalar(1) / numext::real(m_invdiag(j));
        }
        else
        {
            for (Index j = 0; j < mat.outerSize(); ++j)
            {
                RealScalar sum = mat.col(j).squaredNorm();
                if (sum > RealScalar(0))
                    m_invdiag(j) = RealScalar(1) / sum;
                else
                    m_invdiag(j) = RealScalar(1);
            }
        }
        Base::m_isInitialized = true;
        return *this;
    }

    template <typename MatType> LeastSquareDiagonalPreconditioner& compute(const MatType& mat) { return factorize(mat); }

    ComputationInfo info() { return Success; }

protected:
};

/** \ingroup IterativeLinearSolvers_Module
  * \brief A naive preconditioner which approximates any matrix as the identity matrix
  *
  * \implsparsesolverconcept
  *
  * \sa class DiagonalPreconditioner
  */
class IdentityPreconditioner
{
public:
    IdentityPreconditioner() {}

    template <typename MatrixType> explicit IdentityPreconditioner(const MatrixType&) {}

    template <typename MatrixType> IdentityPreconditioner& analyzePattern(const MatrixType&) { return *this; }

    template <typename MatrixType> IdentityPreconditioner& factorize(const MatrixType&) { return *this; }

    template <typename MatrixType> IdentityPreconditioner& compute(const MatrixType&) { return *this; }

    template <typename Rhs> inline const Rhs& solve(const Rhs& b) const { return b; }

    ComputationInfo info() { return Success; }
};

}  // end namespace Eigen

#endif  // EIGEN_BASIC_PRECONDITIONERS_H
